Non-autonomous Ornstein-Uhlenbeck equations in exterior domains

In this paper, we consider non-autonomous Ornstein-Uhlenbeck operators in smooth exterior domains $Ω\subset \R^d$ subject to Dirichlet boundary conditions. Under suitable assumptions on the coefficients, the solution of the corresponding non-autonomous parabolic Cauchy problem is governed by an evolution system $\{P_Ω(t,s)\}_{0\leq s\leq t}$ on $L^p(Ω)$ for $1< p < \infty$. Furthermore, $L^p$-estimates for spatial derivatives and $L^p$-$L^q$ smoothing properties of $P_Ω(t,s)$, $0\leq s\leq t$, are obtained.

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